The invention is based on an electromagnetically actuatable fuel injection valve as defined hereinafter. European Patent Disclosure 0 350 885 A2 has already disclosed an electromagnetically actuatable fuel injection valve that has an inner pole, surrounded by a magnet coil, and an armature that is oriented toward the inner pole and is joined to a ball serving as a valve closing body. The ball is slidably supported in a guide bore and cooperates with a fixed valve seat. Since the ball is slidably supported over its entire circumference in the guide bore, the fuel must be guided around the outside circumference of the swirl element having the guide bore. As a result, the known fuel injection valve has a large outside diameter, so that the compactness demanded for fuel injection valves cannot be attained.